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A025609
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Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner.
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3
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0, 1, 6, 64, 720, 9136, 122016, 1673344, 23216640, 323773696, 4525272576, 63308468224, 886046453760, 12403017773056, 173632453287936, 2430795572936704, 34030785382318080, 476428879520137216, 6669991618287108096, 93379806486052470784, 1307316833784928665600
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OFFSET
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0,3
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COMMENTS
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Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-44,-168).
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FORMULA
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G.f.: x*(1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).
a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3.
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MATHEMATICA
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CoefficientList[ Series[(x - 12 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]
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PROG
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(PARI) concat([0], Vec((1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)))
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CROSSREFS
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Cf. A025607, A025608.
Sequence in context: A237357 A230282 A186668 * A309186 A156887 A239847
Adjacent sequences: A025606 A025607 A025608 * A025610 A025611 A025612
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KEYWORD
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nonn,walk
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AUTHOR
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David W. Wilson
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EXTENSIONS
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Terms a(17) and beyond from Andrew Howroyd, Nov 05 2019
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STATUS
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approved
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